3.12.43 \(\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx\) [1143]

Optimal. Leaf size=34 \[ -\frac {7}{243} (2+3 x)^9+\frac {37}{270} (2+3 x)^{10}-\frac {10}{297} (2+3 x)^{11} \]

[Out]

-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11

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Rubi [A]
time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78} \begin {gather*} -\frac {10}{297} (3 x+2)^{11}+\frac {37}{270} (3 x+2)^{10}-\frac {7}{243} (3 x+2)^9 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^8+\frac {37}{9} (2+3 x)^9-\frac {10}{9} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {7}{243} (2+3 x)^9+\frac {37}{270} (2+3 x)^{10}-\frac {10}{297} (2+3 x)^{11}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 62, normalized size = 1.82 \begin {gather*} 768 x+4480 x^2+\frac {42752 x^3}{3}+24576 x^4+\frac {62496 x^5}{5}-41328 x^6-110160 x^7-133164 x^8-92421 x^9-\frac {356481 x^{10}}{10}-\frac {65610 x^{11}}{11} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9
- (356481*x^10)/10 - (65610*x^11)/11

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Maple [A]
time = 0.08, size = 55, normalized size = 1.62

method	result	size
gosper	\(-\frac {x \left (1968300 x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}[phone] x^{6}[phone] x^{5}-4124736 x^{4}-8110080 x^{3}-4702720 x^{2}-1478400 x -253440\right )}{330}\)	\(54\)
default	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)
norman	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)
risch	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(2+3*x)^8*(3+5*x),x,method=_RETURNVERBOSE)

[Out]

-65610/11*x^11-356481/10*x^10-92421*x^9-133164*x^8-110160*x^7-41328*x^6+62496/5*x^5+24576*x^4+42752/3*x^3+4480
*x^2+768*x

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Maxima [A]
time = 0.33, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="maxima")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

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Fricas [A]
time = 1.10, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="fricas")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (29) = 58\).
time = 0.03, size = 60, normalized size = 1.76 \begin {gather*} - \frac {65610 x^{11}}{11} - \frac {356481 x^{10}}{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac {62496 x^{5}}{5} + 24576 x^{4} + \frac {42752 x^{3}}{3} + 4480 x^{2} + 768 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)**8*(3+5*x),x)

[Out]

-65610*x**11/11 - 356481*x**10/10 - 92421*x**9 - 133164*x**8 - 110160*x**7 - 41328*x**6 + 62496*x**5/5 + 24576
*x**4 + 42752*x**3/3 + 4480*x**2 + 768*x

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Giac [A]
time = 1.23, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="giac")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

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Mupad [B]
time = 0.06, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610\,x^{11}}{11}-\frac {356481\,x^{10}}{10}-92421\,x^9-133164\,x^8-110160\,x^7-41328\,x^6+\frac {62496\,x^5}{5}+24576\,x^4+\frac {42752\,x^3}{3}+4480\,x^2+768\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)*(3*x + 2)^8*(5*x + 3),x)

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9
- (356481*x^10)/10 - (65610*x^11)/11

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